Value-at-Risk Bounds with Two-Sided Dependence Information

Lux, Thibaut; Rüschendorf, Ludger

doi:10.2139/ssrn.3086256

Cited by 5 publications

(7 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…the set of continuous, lower semicontinuous, and upper semicontinuous functions, respectively, with at most linear growth. We then adapt the model-independent super-hedging duality results from, e.g., [1], [12], [19], [21], [26], [49], and [73], to our situation by formulating the following theorem.…”

Section: Setting and Duality Resultsmentioning

confidence: 99%

Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information

Ansari¹,

Lütkebohmert²,

Neufeld³

et al. 2022

Preprint

View full text Add to dashboard Cite

We show how inter-asset dependence information derived from observed market prices of liquidly traded options can lead to improved model-free price bounds for multi-asset derivatives. Depending on the type of the observed liquidly traded option, we either extract correlation information or we derive restrictions on the set of admissible copulas that capture the inter-asset dependencies. To compute the resultant price bounds for some multi-asset options of interest, we apply a modified martingale optimal transport approach. In particular, we derive an adjusted pricing-hedging duality. Several examples based on simulated and real market data illustrate the improvement of the obtained price bounds and thus provide evidence for the relevance and tractability of our approach.

show abstract

Section: Setting and Duality Resultsmentioning

confidence: 99%

Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information

Ansari¹,

Lütkebohmert²,

Neufeld³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Remark 2.4. The optimal transport duality under additional information (2.1) appears in a similar form in Lux and Rüschendorf [20,Theorem 3.2]. These two results were developed in parallel, however their proofs are completely different.…”

Section: Transport and Relaxed Transport Duality Under Additional Inf...mentioning

confidence: 88%

“…These two results were developed in parallel, however their proofs are completely different. Moreover, in [20] the authors consider the Fréchet class of d-dimensional probability distributions with given marginals, whose copulas are bounded from below and above by arbitrary quasi-copulas; a quasi-copula generalizes the notion of a copula. In view of (2.1), our formulation is slightly more general as we do not require the bounds (π i , π i ) i∈I to have a particular structure as imposed by a quasi-copula.…”

Section: Transport and Relaxed Transport Duality Under Additional Inf...mentioning

confidence: 99%

Marginal and dependence uncertainty: bounds, optimal transport, and sharpness

Bartl¹,

Kupper²,

Lux³

et al. 2017

Preprint

Self Cite

View full text Add to dashboard Cite

Motivated by applications in model-free finance and quantitative risk management, we consider Fréchet classes of multivariate distribution functions where additional information on the joint distribution is assumed, while uncertainty in the marginals is also possible. We derive optimal transport duality results for these Fréchet classes that extend previous results in the related literature. These proofs are based on representation results for increasing convex functionals and the explicit computation of the conjugates. We show that the dual transport problem admits an explicit solution for the function f = 1B, where B is a rectangular subset of R d , and provide an intuitive geometric interpretation of this result. The improved Fréchet-Hoeffding bounds provide ad-hoc upper bounds for these Fréchet classes. We show that the improved Fréchet-Hoeffding bounds are pointwise sharp for these classes in the presence of uncertainty in the marginals, while a counterexample yields that they are not pointwise sharp in the absence of uncertainty in the marginals, even in dimension 2. The latter result sheds new light on the improved Fréchet-Hoeffding bounds, since Tankov [30] has showed that, under certain conditions, these bounds are sharp in dimension 2.

show abstract

“…Remark 2.4. The optimal transport duality under additional information (2.2) appears in a similar form in [22,Theorem 3.2]. These two results were developed in parallel; however, their proofs are completely different.…”

Section: Introductionmentioning

confidence: 95%

Marginal and Dependence Uncertainty: Bounds, Optimal Transport, and Sharpness

Bartl¹,

Kupper²,

Lux³

et al. 2022

SIAM J. Control Optim.

Self Cite

View full text Add to dashboard Cite

Motivated by applications in model-free finance and quantitative risk management, we consider Fr\' echet classes of multivariate distribution functions where additional information on the joint distribution is assumed, while uncertainty in the marginals is also possible. We derive optimal transport duality results for these Fr\' echet classes that extend previous results in the related literature. These proofs are based on representation results for convex increasing functionals and the explicit computation of the conjugates. We show that the dual transport problem admits an explicit solution for the function f = 1 B , where B is a rectangular subset of \BbbR d , and provide an intuitive geometric interpretation of this result. The improved Fr\' echet--Hoeffding bounds provide ad hoc bounds for these Fr\' echet classes. We show that the improved Fr\' echet--Hoeffding bounds are pointwise sharp for these classes in the presence of uncertainty in the marginals, while a counterexample yields that they are not pointwise sharp in the absence of uncertainty in the marginals, even in dimension 2. The latter result sheds new light on the improved Fr\' echet--Hoeffding bounds, since Tankov [J. Appl. Probab., 48 (2011), pp. 389--403] has showed that, under certain conditions, these bounds are sharp in dimension 2.

show abstract

Value-at-Risk Bounds with Two-Sided Dependence Information

Cited by 5 publications

References 24 publications

Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information

Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information

Marginal and dependence uncertainty: bounds, optimal transport, and sharpness

Marginal and Dependence Uncertainty: Bounds, Optimal Transport, and Sharpness

Contact Info

Product

Resources

About